Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies – A general framework published in Biomedical Optics Express

Different sampling methods for the trajectory of a particle. (Adapted from the manuscript.)
Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies — A general framework
Laura Pérez-García, Martin Selin, Antonio Ciarlo, Alessandro Magazzù, Giuseppe Pesce, Antonio Sasso, Giovanni Volpe, Isaac Pérez Castillo, Alejandro V. Arzola
Biomedical Optics Express, 14, 6442-6469 (2023)
doi: 10.1364/BOE.495468
arXiv: 2305.07245

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector’s finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Roadmap for Optical Tweezers published in Journal of Physics: Photonics

Illustration of an optical tweezers holding a particle. (Image by A. Magazzù.)
Roadmap for optical tweezers
Giovanni Volpe, Onofrio M Maragò, Halina Rubinsztein-Dunlop, Giuseppe Pesce, Alexander B Stilgoe, Giorgio Volpe, Georgiy Tkachenko, Viet Giang Truong, Síle Nic Chormaic, Fatemeh Kalantarifard, Parviz Elahi, Mikael Käll, Agnese Callegari, Manuel I Marqués, Antonio A R Neves, Wendel L Moreira, Adriana Fontes, Carlos L Cesar, Rosalba Saija, Abir Saidi, Paul Beck, Jörg S Eismann, Peter Banzer, Thales F D Fernandes, Francesco Pedaci, Warwick P Bowen, Rahul Vaippully, Muruga Lokesh, Basudev Roy, Gregor Thalhammer-Thurner, Monika Ritsch-Marte, Laura Pérez García, Alejandro V Arzola, Isaac Pérez Castillo, Aykut Argun, Till M Muenker, Bart E Vos, Timo Betz, Ilaria Cristiani, Paolo Minzioni, Peter J Reece, Fan Wang, David McGloin, Justus C Ndukaife, Romain Quidant, Reece P Roberts, Cyril Laplane, Thomas Volz, Reuven Gordon, Dag Hanstorp, Javier Tello Marmolejo, Graham D Bruce, Kishan Dholakia, Tongcang Li, Oto Brzobohatý, Stephen H Simpson, Pavel Zemánek, Felix Ritort, Yael Roichman, Valeriia Bobkova, Raphael Wittkowski, Cornelia Denz, G V Pavan Kumar, Antonino Foti, Maria Grazia Donato, Pietro G Gucciardi, Lucia Gardini, Giulio Bianchi, Anatolii V Kashchuk, Marco Capitanio, Lynn Paterson, Philip H Jones, Kirstine Berg-Sørensen, Younes F Barooji, Lene B Oddershede, Pegah Pouladian, Daryl Preece, Caroline Beck Adiels, Anna Chiara De Luca, Alessandro Magazzù, David Bronte Ciriza, Maria Antonia Iatì, Grover A Swartzlander Jr
Journal of Physics: Photonics 2(2), 022501 (2023)
arXiv: 2206.13789
doi: 110.1088/2515-7647/acb57b

Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects, ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved into sophisticated instruments and have been employed in a broad range of applications in the life sciences, physics, and engineering. These include accurate force and torque measurement at the femtonewton level, microrheology of complex fluids, single micro- and nano-particle spectroscopy, single-cell analysis, and statistical-physics experiments. This roadmap provides insights into current investigations involving optical forces and optical tweezers from their theoretical foundations to designs and setups. It also offers perspectives for applications to a wide range of research fields, from biophysics to space exploration.

Giuseppe Pesce joins the Soft Matter Lab

(Photo by A. Argun.)
Giuseppe Pesce starts his employment as a researcher at the Physics Department of the University of Gothenburg on 30th March 2022.

Giuseppe has a PhD degree in Physics from the University of Naples, Italy, where he was working for several years. His field of expertise is laser spectroscopy and optical tweezers used for several experiments, in particular for microrheology and statistical mechanics.

During his employment, Giuseppe will work on a project about optical tweezers combined with deep learning for construction of scalable quantum dots arrays and on automatisation of a double optical tweezers system to stretch biomolecules.

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications accepted on Advances in Optics and Photonics

Schematic of a bistable potential generated with a double-beam optical tweezers.

Optical Tweezers: A Comprehensive Tutorial from Calibration to Applications
Jan Gieseler, Juan Ruben Gomez-Solano, Alessandro Magazzù, Isaac Pérez Castillo, Laura Pérez García, Marta Gironella-Torrent, Xavier Viader-Godoy, Felix Ritort, Giuseppe Pesce, Alejandro V. Arzola, Karen Volke-Sepulveda & Giovanni Volpe
Advances in Optics and Photonics, 13(1), 74-241 (2021)
doi: https://doi.org/10.1364/AOP.394888
arXiv: 2004.05246

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this Tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future application of optical tweezers. This Tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All the examples are complemented by the sample data and software necessary to reproduce them.

Minimal Microscopic Heat Engine published in Phys. Rev. E

Experimental realization of a minimal microscopic heat engine

Experimental realization of a minimal microscopic heat engine
Aykut Argun, Jalpa Soni, Lennart Dabelow, Stefano Bo, Giuseppe Pesce, Ralf Eichhorn & Giovanni Volpe
Physical Review E 96(5), 052106 (2017)
DOI: 10.1103/PhysRevE.96.052106
arXiv: 1708.07197

Microscopic heat engines are microscale systems that convert energy flows between heat reservoirs into work or systematic motion. We have experimentally realized a minimal microscopic heat engine. It consists of a colloidal Brownian particle optically trapped in an elliptical potential well and simultaneously coupled to two heat baths at different temperatures acting along perpendicular directions. For a generic arrangement of the principal directions of the baths and the potential, the symmetry of the system is broken, such that the heat flow drives a systematic gyrating motion of the particle around the potential minimum. Using the experimentally measured trajectories, we quantify the gyrating motion of the particle, the resulting torque that it exerts on the potential, and the associated heat flow between the heat baths. We find excellent agreement between the experimental results and the theoretical predictions.

Guide to Building Optical Tweezers published in JOSA B

A step-by-step guide to the realisation of advanced optical tweezers

A step-by-step guide to the realisation of advanced optical tweezers
Giuseppe Pesce, Giorgio Volpe, Onofrio M. Maragò, Philip H. Jones, Sylvain Gigan, Antonio Sasso & Giovanni Volpe
Journal of the Optical Society of America B 32(5), B84—B98 (2015)
DOI: 10.1364/JOSAB.32.000B84
arXiv: 1501.07894

Since the pioneering work of Arthur Ashkin, optical tweezers (OT) have become an indispensable tool for contactless manipulation of micro- and nanoparticles. Nowadays OT are employed in a myriad of applications demonstrating their importance. While the basic principle of OT is the use of a strongly focused laser beam to trap and manipulate particles, more complex experimental setups are required to perform novel and challenging experiments. With this article, we provide a detailed step-by-step guide for the construction of advanced optical manipulation systems. First, we explain how to build a single-beam OT on a homemade micro- scope and how to calibrate it. Improving on this design, we realize a holographic OT, which can manipulate independently multiple particles and generate more sophisticated wavefronts such as Laguerre–Gaussian beams. Finally, we explain how to implement a speckle OT, which permits one to employ random speckle light fields for deterministic optical manipulation.

Longterm Influence of Fluid Inertia on Brownian Motion published in Phys. Rev. E

Longterm influence of fluid inertia on the diffusion of a Brownian particle

Longterm influence of fluid inertia on the diffusion of a Brownian particle
Giuseppe Pesce, Giorgio Volpe, Giovanni Volpe & Antonio Sasso
Physical Review E 90(4), 042309 (2014)
DOI: 10.1103/PhysRevE.90.042309
arXiv: 1402.6913

We experimentally measure the effects of fluid inertia on the diffusion of a Brownian particle at very long time scales. In previous experiments, the use of standard optical tweezers introduced a cutoff in the free diffusion of the particle, which limited the measurement of these effects to times comparable with the relaxation time of the fluid inertia, i.e., a few milliseconds. Here, by using blinking optical tweezers, we detect these inertial effects on time scales several orders longer up to a few seconds. The measured mean square displacement of a freely diffusing Brownian particle in a liquid shows a deviation from the Einstein-Smoluchowsky theory that diverges with time. These results are consistent with a generalized theory that takes into account not only the particle inertia but also the inertia of the surrounding fluid.

Stratonovich-to-Itô Transition published in Nature Commun.

Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

Stratonovich-to-Itô transition in noisy systems with multiplicative feedback
Giuseppe Pesce, Austin McDaniel, Scott Hottovy, Jan Wehr & Giovanni Volpe
Nature Communications 4, 2733 (2013)
DOI: 10.1038/ncomms3733
arXiv: 1206.6271

Intrinsically noisy mechanisms drive most physical, biological and economic phenomena. Frequently, the system’s state influences the driving noise intensity (multiplicative feedback). These phenomena are often modelled using stochastic differential equations, which can be interpreted according to various conventions (for example, Itô calculus and Stratonovich calculus), leading to qualitatively different solutions. Thus, a stochastic differential equation–convention pair must be determined from the available experimental data before being able to predict the system’s behaviour under new conditions. Here we experimentally demonstrate that the convention for a given system may vary with the operational conditions: we show that a noisy electric circuit shifts from obeying Stratonovich calculus to obeying Itô calculus. We track such a transition to the underlying dynamics of the system and, in particular, to the ratio between the driving noise correlation time and the feedback delay time. We discuss possible implications of our conclusions, supported by numerics, for biology and economics.

Work Done by Rotational Force Fields published in J. Opt.

Influence of rotational force fields on the determination of the work done on a driven Brownian particle

Influence of rotational force fields on the determination of the work done on a driven Brownian particle
Giuseppe Pesce, Giovanni Volpe, Alberto Imparato, Giulia Rusciano & Antonio Sasso
Journal of Optics 13(4), 044006 (2011)
DOI: 10.1088/2040-8978/13/4/044006
arXiv: 1006.4534

For a Brownian system the evolution of thermodynamic quantities is a stochastic process, in particular the work performed on a driven colloidal particle held in an optical trap, changes for each realization of the experimental manipulation, even though the manipulation protocol remains unchanged. Nevertheless, the work distribution is governed by established laws. Here, we show how the measurement of the work distribution is influenced by the presence of rotational, i.e. nonconservative, radiation forces. Experiments on particles of different materials show that the rotational radiation forces, and therefore their effect on the work distributions, increase with the particle’s refractive index.

Non-conservative Forces in Optical Traps published in EPL

Quantitative assessment of non-conservative radiation forces in an optical trap

Quantitative assessment of non-conservative radiation forces in an optical trap
Giuseppe Pesce, Giorgio Volpe, Anna Chiara De Luca, Giulia Rusciano & Giovanni Volpe
EPL (Europhysics Letters) 86(3), 38002 (2009)
DOI: 10.1209/0295-5075/86/38002
arXiv: 0902.4178

The forces acting on an optically trapped particle are usually assumed to be conservative. However, the presence of a non-conservative component has recently been demonstrated. Here, we propose a technique that permits one to quantify the contribution of such a non-conservative component. This is an extension of a standard calibration technique for optical tweezers and, therefore, can easily become a standard test to verify the conservative optical force assumption. Using this technique, we have analyzed optically trapped particles of different size under different trapping conditions. We conclude that the non-conservative effects are effectively negligible and do not affect the standard calibration procedure, unless for extremely low-power trapping, far away from the trapping regimes usually used in experiments.